Thiago Trafane Oliveira Santos, Daniel Oliveira Cajueiro
arXiv 16 Sep 2024 · Statistics — Methodology
arXiv:2409.10448 · PDF · DOI · OpenAlex · Extracted main text
Even though practitioners often estimate Pareto exponents running OLS rank-size regressions, the usual recommendation is to use the Hill MLE with a small-sample correction instead, due to its unbiasedness and efficiency. In this paper, we advocate that you should also apply OLS in empirical applications. On the one hand, we demonstrate that, with a small-sample correction, the OLS estimator is also unbiased. On the other hand, we show that the MLE assigns significantly greater weight to smaller observations. This suggests that the OLS estimator may outperform the MLE in cases where the distribution is (i) strictly Pareto but only in the upper tail or (ii) regularly varying rather than strictly Pareto. We substantiate our theoretical findings with Monte Carlo simulations and real-world applications, demonstrating the practical relevance of the OLS method in estimating tail exponents.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
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| 7 | Gabaix (1999) `Zipf's law for cities: An explanation', The Quarterly Journal of Economics 114(3), 739–767 | 0.644 | 2 | 2 | 100% |
| 8 | Gabaix \ Ioannides (2004) The Evolution of City Size Distributions, Vol. 4, North-Holland, chapter 53, pp. 2341–2378 | 0.644 | 2 | 2 | 100% |
| 9 | Gopikrishnan, Plerou, Amaral, Meyer \ Stanley (1999) `Scaling of the distribution of fluctuations of financial market indices', Physical Review E 60(5), 5305–5316 | 0.644 | 2 | 2 | 100% |
| 10 | Gabaix (2009) `Power laws in economics and finance', Annual Review of Economics 1(1), 255–293 | 0.585 | 3 | 1 | 100% |
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